Spiral groove milling curved surface point cloud simulation calculation method based on intersection points

Abstract

The invention discloses a spiral groove milling curved surface point cloud simulation calculation method based on intersection points, and the method specifically comprises the steps: firstly, constructing a tool general parameterized model; then, a cutter milling kinematics model is constructed and used for guiding the milling process, and the milling mode of the spiral groove is achieved; secondly, solving a spiral groove milling curved surface point cloud model based on an envelope principle; and finally, carrying out reconstruction calculation on the point cloud model through point cloud intersection point calculation and a point cloud selection principle, and carrying out comparison verification on the calculated spiral groove milling curved surface point cloud simulation model and a model after importing a cutter milling track and a geometric shape into Veicut to carry out spiral groove curved surface simulation. According to the method, high-precision visual display is carried out on spiral groove milling curved surface point cloud simulation, and correctness and effectiveness of related theories of the method are proved.

Description

Technical Field

[0001] This invention belongs to the field of CNC milling simulation technology, and particularly relates to a point cloud simulation calculation method for spiral groove milling surface based on intersection points. Background Technology

[0002] Helical grooves are a key structure of CNC cutting tools, determining their cutting performance, rigidity, and strength. Visual simulation of the milled surface after helical groove milling provides an intuitive understanding of the rationality of the structural and process parameters. This is particularly important for structures formed by the superposition of two or more helical grooves, which are often difficult to predict directly and require the use of other 3D simulation milling software, such as NUMROTOplus from NUM (Switzerland), VirtualGrind from Rollomatic, and Helitronic Tool studio from Walter (Germany). Compared to using these mature commercial simulation software, point cloud simulation of the milled surface of helical grooves offers a more intuitive and comprehensive analysis of the milled surface and allows for rapid adjustment of the structural and process parameters of the helical groove based on the obtained point cloud simulation. Therefore, this invention will combine the kinematic model of the cutting tool to perform point cloud simulation calculations on the milled surface of the helical groove.

[0003] Existing simulation machining technologies mainly rely on hybrid programming techniques for end mill machining using OpenGL and Matlab, Vericut simulation technology, and simulation technology based on secondary development of 3D software. Chen Fengjun utilized VC++ to call COM components to access various MATLAB function libraries and employed joint programming of OpenGL and VC++ to achieve 3D animation simulation of ball end mill machining. Xiong Feng et al. used the Matlab graphics processing development platform to realize milling simulation of complex-shaped tools. He Feng used Qt as the interface development tool and OpenGL programming technology to realize geometric models and animation simulation, developing applications using KDevelop as the integrated development environment. He Lin et al. used SolidWorks secondary development technology, utilizing SolidWorks' solid modeling capabilities, Boolean difference operations between entities, and a system interface developed in VB to establish a machining simulation system for the rake face of the ball end mill's end cutting edge. Zhao Bang used UG secondary development technology, enabling designers to obtain the tool's motion trajectory and posture during the milling process during the design phase. By simulating the machining motion, interference between the tool and the milling cutter can be effectively avoided. Liu Jianjun et al. established a simulation platform for end mill machining based on the virtual simulation environment of VERICUT software. Their point cloud simulation calculation method, based on the envelope principle, directly calculates the simulation of the spiral groove milling surface through the tool's milling kinematic model. This not only reduces the difficulty of simulation development but also facilitates the provision of visual basis for adjusting process parameters. However, the point cloud simulation and point cloud overlay solution algorithms are still not perfect. Summary of the Invention

[0004] To address the above problems, this invention provides a point cloud simulation calculation method for spiral groove milling surfaces based on intersection points.

[0005] The present invention provides a point cloud simulation calculation method for a spiral groove milled surface based on intersection points, comprising the following steps:

[0006] Step 1: Establish the coordinate system and the general geometric model of the tool.

[0007] Workpiece Coordinate System (WCS):

[0008] Define the workpiece coordinate system as O W -X W Y W Z W Its coordinate origin O is the center of the circle on the end face of the workpiece. W The starting point of the cylindrical helical cutting edge is located on the X-axis. W Above, the tool axis and the coordinate axis Z W coincide.

[0009] Tool Coordinate System (GCS):

[0010] Define the tool coordinate system as O G -X G Y G Z G Tool rotation axis and coordinate axis Z G Coincidence, the tool tip plane coincides with the coordinate system plane X G Y G coincide.

[0011] Establish a general geometric model for the cutting tool:

[0012] Define the two end faces of the tool and the coordinate plane X G Y G The distances are H0 and H1, respectively, meaning the effective width range of the tool rotation profile is [H0, H1].

[0013] When constructing the tool rotation profile, the tool is discretized into pieces along the tool axis to construct the complete tool rotation profile; the tool rotation profile curve is defined as m, and point P is set. m Let H be any point on the tool's rotational profile, with a rotational radius of R(h), and perpendicular to the coordinate system plane X. G Y G The distance is h, and the line segment O G P m With coordinate axis X G The included angle is the tool rotation angle. Then point P m The coordinates are expressed in the tool coordinate system as follows:

[0014]

[0015] Step 2: Establish the tool kinematics model.

[0016] (1) Definition of the initial milling pose of the tool.

[0017] Define the origin O of the cutting tool when it is in the initial milling pose. G Located in X W On the coordinate axis and at the origin O W The distance is d X coordinate axis X G With X W Consistent direction, coordinate axis Z G With Z W The included angle is the tool mounting angle α.

[0018] The geometric transformation relationship between the tool coordinate system (GCS) and the workpiece coordinate system (WCS) corresponding to the initial milling pose is expressed as a rotation matrix R. x Translation vector T x .

[0019]

[0020] (2) Expression of milling motion of cutting tool.

[0021] The milling trajectory is defined as a conical helical motion. The milling process of the helical groove is considered as the tool remaining stationary while performing conical helical motion based on its initial milling pose; this motion process is described by the tool origin O. G It performs a conical-helical motion relative to the workpiece coordinate system WCS.

[0022] Define coordinate system GCS around coordinate axis Z W The angle of rotation is the helical rotation angle ξ of the tool, i.e., the angle of rotation of line segment O. W O G In the coordinate plane X W Y W Projection onto the coordinate axis X W The included angle; assuming the tool performs a constant-lead conical helical motion relative to itself, the lead of the tool's helical motion is defined as p. h The cone angle of the spiral motion is κ. G Its value is related to the cone angle κ of the conical spiral groove core. c If they are equal, then the rotation angle ξ of the tool's helical motion can be expressed as:

[0023]

[0024] In the formula, z p O is the origin of the tool coordinate system G The axial movement distance.

[0025] Assuming the tool is along the coordinate axis Z T The unit rotation angle of the moving tool's helical motion is k. ξ Then equation (3) can be further expressed as:

[0026] ξ=k ξ z p (4)

[0027] Let the origin of the tool be O. G The distances traveled relative to the workpiece coordinate system WCS are Δx, Δy, and Δz, respectively, i.e.:

[0028]

[0029] The position of the milling motion of the tool is expressed by a rotation matrix and a translation vector, as shown below:

[0030]

[0031] Therefore, according to equations (2) and (6), the pose transformation of the milling motion of the tool is divided into a rotation matrix M = (p,n,v) and a translation matrix r, expressed as:

[0032]

[0033] When the tool is in its initial position, the tool coordinate system coincides with the axial section coordinate system, and the tool origin and axis vector are (0,0,0) at this time. T and (0,0,1) T According to equation (7), the tool origin O G Coordinates and tool axis vector Z G The coordinates in the workpiece coordinate system WCS are expressed as follows:

[0034]

[0035] Furthermore, by combining equations (4)-(6), we know that during the milling process, any point P on the tool's rotating surface... m The coordinates are expressed in the WCS coordinate system as:

[0036]

[0037] Step 3: Calculate the point cloud of the milled spiral groove surface.

[0038] The motion trajectory formed by the set of points on the tool surface is defined as the milling curve, denoted as C. t All milling curves form a family of milling curves; by definition, the first two lines of equation (9) constitute the parametric equations of the milling curves, and the parametric equations of the milling curves are expressed as:

[0039]

[0040] In the formula, h∈(H0,H1) is a parameter of the milling curve family. It is a parameter of a milling curve.

[0041] When the Z coordinate in equation (9) is set to a constant C, the variable ξ is solved as shown in equation (11). Then, the variable ξ is substituted into equation (10) to obtain the family of milling curves in the workpiece coordinate system with an axial distance of C in the plane.

[0042]

[0043] The envelope curve of the milling curve family is the curve tangent to each milling curve. Each tangency point is defined as an envelope point. The envelope points under each cross section form an envelope line, which is the cross-sectional profile of the helical groove after milling by the tool under that cross section. According to the envelope principle, the envelope curve should satisfy the parametric equation shown in equation (12):

[0044]

[0045] In the formula, the milling curve family parameter h∈(H0,H1), the milling curve parameter

[0046] The envelope curve of the milling curve family within an arbitrary cross section with an axial distance of C is obtained by solving equation (12). Since equation (12) is highly nonlinear and difficult to solve, the objective function in equation (13) is constructed, and the milling curve parameters that satisfy the envelope condition are obtained. The envelope point can be obtained by solving for each h in the interval [H0,H1] using an intelligent algorithm. Substituting into equation (10), we obtain its parametric equation as shown in equation (14).

[0047]

[0048] In the formula, n is the number of tool discrete along the axial direction.

[0049] The point cloud simulation diagram of the helical groove milled surface can be obtained by combining the envelope point curves formed by the envelope points in all the calculated axial sections according to their corresponding axial distances. The point cloud of the helical groove milled surface is then represented as follows:

[0050]

[0051] Step 4: Simulation calculation of point cloud for helical groove milling surface based on point cloud reconstruction.

[0052] For a single spiral groove, steps 1-3 are sufficient to solve the simulation of the point cloud of its milled surface.

[0053] For double helical grooves, the intersection of the point clouds of the two helical grooves is solved, and the two parts of the helical groove point cloud are reconstructed to achieve simulation of the milled surface of the double helical groove in the form of point cloud.

[0054] (1) Judgment and solution of intersection points of point cloud of double helical groove surface.

[0055] From equation (14), the point cloud of the helical groove in any axial section is obtained. The envelope curves of the cross-sectional profiles of the two helical grooves in the axial section with an axial distance of C1 are defined as follows: Two adjacent points in the envelope curve of f Connect the points to form vector AB, and let point A be an adjacent point on the curve containing the envelope of f1. Connect the lines to form vectors AC and AD. Perform cross products of vector AB with AC and AD respectively, then multiply the results. Determine if the two envelope curves intersect by checking if the result is less than 0. The expression is as follows:

[0056] (AB×AC)·(AB×AD)<0 (16)

[0057] Equation (16) is used to determine whether there is an intersection point between the cross-sectional contour envelope curves of the two helical grooves within an axial section with an axial distance of C1, and the coordinates of the intersection point are further calculated as follows:

[0058]

[0059] In the formula x A ,y A ,x B ,y B ,x C ,y C ,x D ,y D These are the x and y coordinates of points A, B, C, and D, respectively.

[0060] (2) Selection principle for reconstructing double helix groove point cloud.

[0061] Since milling removes material, the cross-sectional profile curves of the two helical groove milled surfaces within the same axial section are taken to form the composite helical groove cross-sectional profile curve. The composite helical groove cross-sectional profile curves under different sections can be used to form the point cloud simulation of the surface after double helical groove milling. Thus, the simulation calculation of the point cloud of the surface after double helical groove milling is completed by reconstructing the point clouds of the two helical grooves.

[0062] Assume the initial point of the envelope curve f of the cross-sectional profile of the helical groove. Closer to the axis, the P in the spiral groove envelope curve f sSegment A is part of the composite spiral groove cross-sectional profile curve f*. At the intersection of the two cross-sectional profile curves f and f1, the "right-hand rule" is needed to determine which part of curve f1 belongs to the composite spiral groove cross-sectional profile curve f*. That is, AB is cross-producted with AC and AD respectively. If AB×AC>0, then the distance from point C to the end of curve f1 is... The segment belongs to a part of the composite spiral groove cross-sectional profile curve f*; otherwise, point B is from the starting point of curve f1. The segment is part of the profile curve f* of the composite spiral groove section.

[0063] The beneficial technical effects of this invention compared to the prior art are as follows:

[0064] This invention proposes a point cloud simulation calculation method for helical groove milling surfaces based on intersection points. By constructing a tool kinematics model, the point cloud of the helical groove milling surface is obtained based on envelope theory. Furthermore, the designed point cloud intersection point solution method and point cloud reconstruction selection principle can accurately solve the point cloud simulation of composite surfaces after multi-helical groove milling. This avoids the need for external software for simulation and allows for a faster and more direct display of the milling results. Attached Figure Description

[0065] Figure 1 This is a schematic diagram of the spiral groove and the workpiece coordinate system.

[0066] Figure 2 This is a schematic diagram of the tool coordinate system.

[0067] Figure 3 This is a schematic diagram of the initial milling pose of the cutting tool.

[0068] Figure 4 This is a schematic diagram of the milling motion of the cutting tool.

[0069] Figure 5 This is a schematic diagram of the milling curve of the cutting tool.

[0070] Figure 6 This is a schematic diagram of the envelope of the cross-sectional profile of the spiral groove.

[0071] Figure 7 This is a simulation diagram of the point cloud of a spiral groove milled surface.

[0072] Figure 8 This diagram illustrates the principles for determining, solving, and reconstructing point cloud intersections.

[0073] Figure 9 This is a schematic diagram of a milling tool for spiral grooves.

[0074] Figure 10 This is a simulation diagram of point cloud data for milling a curved surface with a double helical groove.

[0075] Figure 11 This is a simulation diagram of Vericut double helical groove milling surface. Detailed Implementation

[0076] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0077] The present invention provides a point cloud simulation calculation method for a spiral groove milled surface based on intersection points, comprising the following steps:

[0078] Step 1: Establish the coordinate system and the general geometric model of the tool.

[0079] Workpiece Coordinate System (WCS):

[0080] To facilitate the description of the point cloud of the helical groove milled surface and the relative position of the tool with respect to the workpiece, the workpiece coordinate system is defined as O. W -X W Y W Z W ,like Figure 1 As shown, its coordinate origin O is the center of the circle on the end face of the workpiece. W The starting point of the cylindrical helical cutting edge is located on the X-axis. W Above, the tool axis and the coordinate axis Z W coincide.

[0081] Tool Coordinate System (GCS):

[0082] To accurately represent the tool's rotational profile and establish a kinematic model of the tool during milling, the tool coordinate system is defined as O. G -X G Y G Z G ,like Figure 2 As shown, the tool rotation axis and the coordinate axis Z G Coincidence, the tool tip plane coincides with the coordinate system plane X G Y G coincide.

[0083] Establish a general geometric model for the cutting tool:

[0084] Define the two end faces of the tool and the coordinate plane X G Y G The distances are H0 and H1, respectively, meaning the effective width range of the tool rotation profile is [H0, H1].

[0085] When constructing the tool rotation profile, the tool is discretized into pieces along the tool axis to construct the complete tool rotation profile; the tool rotation profile curve is defined as m, and point P is set. m Let H be any point on the tool's rotational profile, with a rotational radius of R(h), and perpendicular to the coordinate system plane X. G YG The distance is h, and the line segment O G P m With coordinate axis X G The included angle is the tool rotation angle. Then point P m The coordinates are expressed in the tool coordinate system as follows:

[0086]

[0087] Step 2: Establish the tool kinematics model.

[0088] (1) Definition of the initial milling pose of the tool.

[0089] To facilitate the description of the tool's position and orientation in the workpiece coordinate system (WCS) and its relative milling motion with the workpiece, the tool's milling pose is described using the geometric relationship between the tool coordinate system (GCS) and the workpiece coordinate system (WC). The origin O of the tool is defined as follows when it is in its initial milling pose: G Located in X W On the coordinate axis and at the origin O W The distance is d X coordinate axis X G With X W Consistent direction, coordinate axis Z G With Z W The included angle is the tool mounting angle α, such as Figure 3 As shown.

[0090] The geometric transformation relationship between the tool coordinate system (GCS) and the workpiece coordinate system (WCS) corresponding to the initial milling pose is expressed as a rotation matrix R. x Translation vector T x .

[0091]

[0092] (2) Expression of milling motion of cutting tool.

[0093] To systematically describe the milling process of a helical groove, the tool milling trajectory is defined as a conical helical motion. The milling process of the helical groove is considered as the tool remaining fixed while performing a conical helical motion based on its initial milling pose; this motion process is described by the tool origin O. G Performing conical-helical motion relative to the workpiece coordinate system WCS, such as... Figure 4 As shown.

[0094] Define coordinate system GCS around coordinate axis Z W The angle of rotation is the helical rotation angle ξ of the tool, i.e., the angle of rotation of line segment O. W O G In the coordinate plane X W Y WProjection onto the coordinate axis X W The included angle; assuming the tool performs a constant-lead conical helical motion relative to itself, the lead of the tool's helical motion is defined as p. h The cone angle of the spiral motion is κ. G Its value is related to the cone angle κ of the conical spiral groove core. c If they are equal, then the rotation angle ξ of the tool's helical motion can be expressed as:

[0095]

[0096] In the formula, z p O is the origin of the tool coordinate system G The axial movement distance.

[0097] Assuming the tool is along the coordinate axis Z T The unit rotation angle of the moving tool's helical motion is k. ξ Then equation (3) can be further expressed as:

[0098] ξ=k ξ z p (4)

[0099] Let the origin of the tool be O. G The distances traveled relative to the workpiece coordinate system WCS are Δx, Δy, and Δz, respectively, i.e.:

[0100]

[0101] The position of the milling motion of the tool is expressed by a rotation matrix and a translation vector, as shown below:

[0102]

[0103] Therefore, according to equations (2) and (6), the pose transformation of the milling motion of the tool is divided into a rotation matrix M = (p,n,v) and a translation matrix r, expressed as:

[0104]

[0105] When the tool is in its initial position, the tool coordinate system coincides with the axial section coordinate system, and the tool origin and axis vector are (0,0,0) at this time. T and (0,0,1) T According to equation (7), the tool origin O G Coordinates and tool axis vector Z G The coordinates in the workpiece coordinate system WCS are expressed as follows:

[0106]

[0107] Furthermore, by combining equations (4)-(6), we know that during the milling process, any point P on the tool's rotating surface...m The coordinates are expressed in the WCS coordinate system as:

[0108]

[0109] Step 3: Calculate the point cloud of the milled spiral groove surface.

[0110] The motion trajectory formed by the set of points on the tool surface is defined as the milling curve, denoted as C. t All milling curves form a family of milling curves, such as Figure 5 As shown. By definition, the first two lines of equation (9) constitute the parametric equation of the milling curve, and the parametric equation of the milling curve is expressed as:

[0111]

[0112] In the formula, h∈(H0,H1) is a parameter of the milling curve family. It is a parameter of a milling curve.

[0113] When the Z coordinate in equation (9) is set to a constant C, the variable ξ is solved as shown in equation (11). Then, the variable ξ is substituted into equation (10) to obtain the family of milling curves in the workpiece coordinate system with an axial distance of C in the plane.

[0114]

[0115] The envelope curve of the milling curve family is the curve tangent to each milling curve. Each point of tangency is defined as an envelope point. The envelope points under each cross section form an envelope line, which is the cross-sectional profile of the helical groove after milling by the tool under that cross section, such as... Figure 6 As shown. According to the envelope principle, the envelope curve should satisfy the parametric equation shown in equation (12):

[0116]

[0117] In the formula, the milling curve family parameter h∈(H0,H1), the milling curve parameter

[0118] The envelope curve of the milling curve family within an arbitrary cross section with an axial distance of C is obtained by solving equation (12). Since equation (12) is highly nonlinear and difficult to solve, the objective function in equation (13) is constructed, and the milling curve parameters that satisfy the envelope condition are obtained. The envelope point can be obtained by solving for each h in the interval [H0,H1] using an intelligent algorithm. Substituting into equation (10), we obtain its parametric equation as shown in equation (14).

[0119]

[0120] In the formula, n is the number of tool discrete along the axial direction.

[0121] By combining the envelope point curves formed by the calculated envelope points within all axial sections according to their corresponding axial distances, a point cloud simulation image of the helical groove milling surface can be obtained, such as... Figure 7 As shown, the point cloud of the milled spiral groove surface is represented as follows:

[0122]

[0123] Step 4: Simulation calculation of point cloud for helical groove milling surface based on point cloud reconstruction.

[0124] For a single spiral groove, steps 1-3 are sufficient to solve the simulation of the point cloud of its milled surface.

[0125] For double helical grooves, the intersection of the point clouds of the two helical grooves is solved, and the two parts of the helical groove point cloud are reconstructed to achieve simulation of the milled surface of the double helical groove in the form of point cloud.

[0126] (1) Judgment and solution of intersection points of point cloud of double helical groove surface.

[0127] From equation (14), the point cloud of the helical groove in any axial section is obtained. The envelope curves of the cross-sectional profiles of the two helical grooves in the axial section with an axial distance of C1 are defined as follows: like Figure 8 As shown. Points between adjacent points on the envelope curve of f... Connect the points to form vector AB, and let point A be an adjacent point on the curve containing the envelope of f1. Connect the lines to form vectors AC and AD. Perform cross products of vector AB with AC and AD respectively, then multiply the results. Determine if the two envelope curves intersect by checking if the result is less than 0. The expression is as follows:

[0128] (AB×AC)·(AB×AD)<0 (16)

[0129] Equation (16) is used to determine whether there is an intersection point between the cross-sectional contour envelope curves of the two helical grooves within an axial section with an axial distance of C1, and the coordinates of the intersection point are further calculated as follows:

[0130]

[0131] In the formula x A ,y A ,x B ,y B ,x C ,y C ,x D ,y D These are the x and y coordinates of points A, B, C, and D, respectively.

[0132] (2) Selection principle for reconstructing double helix groove point cloud.

[0133] Since milling removes material, the cross-sectional profile curves of the two helical groove milled surfaces within the same axial section are taken to form the composite helical groove cross-sectional profile curve. The composite helical groove cross-sectional profile curves under different sections can be used to form the point cloud simulation of the surface after double helical groove milling. Thus, the simulation calculation of the point cloud of the surface after double helical groove milling is completed by reconstructing the point clouds of the two helical grooves.

[0134] like Figure 8 As shown, assume the initial point of the envelope curve f of the cross-sectional profile of the spiral groove. Closer to the axis, the P in the spiral groove envelope curve f s Segment A is part of the composite spiral groove cross-sectional profile curve f*. At the intersection of the two cross-sectional profile curves f and f1, the "right-hand rule" is needed to determine which part of curve f1 belongs to the composite spiral groove cross-sectional profile curve f*. That is, AB is cross-producted with AC and AD respectively. If AB×AC>0, then the distance from point C to the end of curve f1 is... The segment belongs to a part of the composite spiral groove cross-sectional profile curve f*; otherwise, point B is from the starting point of curve f1. The segment is part of the profile curve f* of the composite spiral groove section.

[0135] Example:

[0136] To verify the correctness of the proposed simulation calculation method for point clouds of helical groove milling surfaces, this embodiment illustrates the feasibility of the proposed method through a set of double-helical milling simulation examples. The relevant helical groove milling process parameters and overall tool parameters are shown in Tables 1 and 2, and the tool shape used is as follows. Figure 9 As shown.

[0137] Table 1 Overall tool parameters and milling process parameters for spiral groove 1

[0138]

[0139] Table 2 Milling process parameters for spiral groove 2

[0140]

[0141] Based on the set helical groove milling process parameters and tool profile, the point clouds of both helical groove surfaces are calculated with the cross-sectional contour envelope points calculated according to the adjacent axial section distance of 0.1mm. All axial section contour envelope points form the helical groove milling surface point cloud. The simulation diagram of the surface point cloud after double helical groove milling is as follows: Figure 10As shown, it can be seen that the principles for judging, solving, and selecting the intersection points of the spiral groove section contour envelope curves under any axially equidistant cross-sections are correct.

[0142] The generated toolpath and tool shape are then imported into the Vericut simulation environment for simulation. The simulation results are as follows: Figure 11 As shown. By comparing the point cloud and the Vericut simulation surface model, it can be seen that the point cloud simulation of the milled surface is highly consistent with the Vericut surface simulation model. The small differences may be due to the low accuracy of the simulation model.

[0143] In summary, by providing the milling parameters and the tool's geometric profile, a point cloud simulation model for helical groove milling was calculated. Multiple calculated helical groove point cloud models were then reconstructed to obtain a final point cloud simulation model for the helical groove milling surface. Comparison of the point cloud model and the Vericut surface simulation model's cross-section shows good consistency between the helical groove point cloud simulation milling cross-section profile curve and the Vericut helical groove milling surface simulation model's cross-section profile curve, verifying the correctness and effectiveness of the intersection-based helical groove milling surface point cloud simulation calculation method.

Claims

1. A method for simulating and calculating point clouds of milled spiral groove surfaces based on intersection points, characterized in that, Includes the following steps: Step 1: Establish the coordinate system and the general geometric model of the tool; Workpiece Coordinate System (WCS): Define the workpiece coordinate system as O W -X W Y W Z W Its coordinate origin O is the center of the circle on the end face of the workpiece. W The starting point of the cylindrical helical cutting edge is located on the X-axis. W Above, the tool axis and the coordinate axis Z W coincide; Tool Coordinate System (GCS): Define the tool coordinate system as O G -X G Y G Z G Tool rotation axis and coordinate axis Z G Coincidence, the tool tip plane and the coordinate system plane X G Y G coincide; Establish a general geometric model for the cutting tool: Define the two end faces of the tool and the coordinate plane X G Y G The distances are H0 and H1, respectively, meaning the effective width range of the tool rotation profile is [H0, H1]. When constructing the tool rotation profile, the tool is discretized into pieces along the tool axis to construct the complete tool rotation profile; the tool rotation profile curve is defined as m, and point P is set. m Let H be any point on the tool's rotational profile, with a rotational radius of R(h), and perpendicular to the coordinate system plane X. G Y G The distance is h, and the line segment O G P m With coordinate axis X G The included angle is the tool rotation angle. Then point P m The coordinates are expressed in the tool coordinate system as follows: Step 2: Establish the tool kinematics model; (1) Definition of the initial milling pose of the tool; Define the origin O of the cutting tool when it is in the initial milling pose. G Located in X W On the coordinate axis and at the origin O W The distance is d X coordinate axis X G With X W Consistent direction, coordinate axis Z G With Z W The included angle is the tool mounting angle α; The geometric transformation relationship between the tool coordinate system (GCS) and the workpiece coordinate system (WCS) corresponding to the initial milling pose is expressed as a rotation matrix R. x Translation vector T x ; (2) Expression of milling motion of the cutting tool; The milling trajectory is defined as a conical helical motion. The milling process of the helical groove is considered as the tool remaining stationary while performing conical helical motion based on its initial milling pose; this motion process is described by the tool origin O. G Performs conical-helical motion relative to the workpiece coordinate system WCS; Define coordinate system GCS around coordinate axis Z W The angle of rotation is the helical rotation angle ξ of the tool, i.e., the angle of rotation of line segment O. W O G In the coordinate plane X W Y W Projection onto the coordinate axis X W The included angle; assuming the tool performs a constant-lead conical helical motion relative to itself, the lead of the tool's helical motion is defined as p. h The cone angle of the spiral motion is κ. G Its value is related to the cone angle κ of the conical spiral groove core. c If they are equal, then the rotation angle ξ of the tool's helical motion can be expressed as: In the formula, z p O is the origin of the tool coordinate system G axial movement distance; Assuming the tool is along the coordinate axis Z T The unit rotation angle of the moving tool's helical motion is k. ξ Then equation (3) can be further expressed as: ξ=k ξ With p (4) Let the origin of the tool be O. G The distances traveled relative to the workpiece coordinate system WCS are Δx, Δy, and Δz, respectively, that is: The position of the milling motion of the tool is expressed by a rotation matrix and a translation vector, as shown below: Therefore, according to equations (2) and (6), the pose transformation of the milling motion of the tool is divided into a rotation matrix M = (p,n,v) and a translation matrix r, expressed as: When the tool is in its initial position, the tool coordinate system coincides with the axial section coordinate system, and the tool origin and axis vector are (0,0,0) at this time. T and (0,0,1) T According to equation (7), the tool origin O G Coordinates and tool axis vector Z G The coordinates in the workpiece coordinate system WCS are expressed as follows: Furthermore, by combining equations (4)-(6), we know that during the milling process, any point P on the tool's rotating surface... m The coordinates in the WCS coordinate system are expressed as: Step 3: Calculate the point cloud of the milled spiral groove surface; The motion trajectory formed by the set of points on the tool surface is defined as the milling curve, denoted as C. t All milling curves form a family of milling curves; by definition, the first two lines of equation (9) constitute the parametric equations of the milling curves, and the parametric equations of the milling curves are expressed as: In the formula, h∈(H0,H1) is a parameter of the milling curve family. It is a parameter of a milling curve; When the Z coordinate in equation (9) is set to a constant C, the variable ξ is solved as shown in equation (11). Then, the variable ξ is substituted into equation (10) to obtain the family of milling curves under the workpiece coordinate system with an axial distance of C. The envelope curve of the milling curve family is the curve tangent to each milling curve. Each tangency point is defined as an envelope point. The envelope points under each cross section form an envelope line, which is the cross-sectional profile of the helical groove after milling by the tool under that cross section. According to the envelope principle, the envelope curve should satisfy the parametric equation shown in equation (12): In the formula, the milling curve family parameter h∈(H0,H1), the milling curve parameter The envelope curve of the milling curve family within an arbitrary cross section with an axial distance of C is obtained by solving equation (12). Since equation (12) is highly nonlinear and difficult to solve, the objective function in equation (13) is constructed, and the milling curve parameters that satisfy the envelope condition are obtained. The envelope point can be obtained by solving for each h in the interval [H0,H1] using an intelligent algorithm. Substituting into equation (10), we obtain its parametric equation as shown in equation (14); In the formula, n is the number of tool discretizations along the axial direction; The point cloud simulation diagram of the helical groove milled surface can be obtained by combining the envelope point curves formed by the envelope points in all the calculated axial sections according to their corresponding axial distances. The point cloud of the helical groove milled surface is then represented as follows: Step 4: Simulation calculation of point cloud for helical groove milling surface based on point cloud reconstruction; For a single spiral groove, steps 1-3 are sufficient to solve the simulation of the point cloud of its milled surface; For double helical grooves, the intersection of the point clouds of the two helical grooves is solved, and the two parts of the helical groove point cloud are reconstructed to achieve simulation of the milled surface of the double helical groove in the form of point cloud. (1) Determining and solving the intersection points of the point cloud of the double helical groove surface; From equation (14), the point cloud of the helical groove in any axial section is obtained. The envelope curves of the cross-sectional profiles of the two helical grooves in the axial section with an axial distance of C1 are defined as follows: Two adjacent points in the envelope curve of f Connect the points to form vector AB, and let point A be an adjacent point on the curve containing the envelope of f1. Connect the lines to form vectors AC and AD. Perform cross products of vector AB with AC and AD respectively, then multiply the results. Determine if the two envelope curves intersect by checking if the result is less than 0. The expression is as follows: (AB×AC)·(AB×AD)<0 (16) Equation (16) is used to determine whether there is an intersection point between the cross-sectional contour envelope curves of the two helical grooves within an axial section with an axial distance of C1, and the coordinates of the intersection point are further calculated as follows: In the formula x A ,y A ,x B ,y B ,x C ,y C ,x D ,y D These are the x and y coordinates of points A, B, C, and D, respectively. (2) Selection principles for reconstructing point clouds in double helix grooves; Since milling has the property of removing material, the cross-sectional profile curves of the two helical groove milling surfaces in the same axial section are taken to form the cross-sectional profile curve of the composite helical groove. The point cloud simulation of the surface after double helical groove milling can be formed by the composite helical groove cross-sectional profile curves under different sections. Thus, the simulation calculation of the point cloud of the surface after double helical groove milling is completed by reconstructing the point clouds of the two helical grooves. Assume the initial point of the envelope curve f of the cross-sectional profile of the helical groove. Closer to the axis, the P in the spiral groove envelope curve f s Segment A is part of the composite spiral groove cross-sectional profile curve f*. At the intersection of the two cross-sectional profile curves f and f1, the "right-hand rule" is needed to determine which part of curve f1 belongs to the composite spiral groove cross-sectional profile curve f*. That is, AB is cross-producted with AC and AD respectively. If AB×AC>0, then the distance from point C to the end of curve f1 is... The segment belongs to a part of the composite spiral groove cross-sectional profile curve f*; otherwise, point B is from the starting point of curve f1. The segment is part of the profile curve f* of the composite spiral groove section.

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